Analysis of Process Flexibility Designs under Disruptions

Most of the previous studies of process flexibility designs have focused on expected sales and demand uncertainty. In this paper, we examine the worst-case performance of flexibility designs in the case of demand and supply uncertainties, where the latter can be in the form of either plant or arc disruptions. We define the Plant Cover … Read more

Approximations for Pareto and Proper Pareto solutions and their KKT conditions

There has been numerous amount of studies on proper Pareto points in multiobjective optimization theory. Geoffrion proper points are one of the most prevalent form of proper optimality. Due to some convergence issues a restricted version of these proper points, Geoffrion proper points with preset bounds has been introduced recently. Since solution of any algorithm … Read more

Low-M-Rank Tensor Completion and Robust Tensor PCA

In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly symmetric M-rank. We discuss the connections between these new tensor ranks and the CP-rank and … Read more

Mathematical models for stable matching problems with ties and incomplete lists

We present new integer linear programming (ILP) models for NP-hard optimisation problems in instances of the Stable Marriage problem with Ties and Incomplete lists (SMTI) and its many-to-one generalisation, the Hospitals / Residents problem with Ties (HRT). These models can be used to efficiently solve these optimisation problems when applied to (i) instances derived from … Read more

Subset selection in sparse matrices

In subset selection we search for the best linear predictor that involves a small subset of variables. From a computational complexity viewpoint, subset selection is NP-hard and few classes are known to be solvable in polynomial time. Using mainly tools from discrete geometry, we show that some sparsity conditions on the original data matrix allow … Read more

Two-stage stochastic days-off scheduling of multi-skilled analysts with training options

Motivated by a cybersecurity application, this paper studies a two-stage, stochastic days-off scheduling problem with 1) many types of jobs that require specialized training, 2) many multi-skilled analysts, 3) the ability to shape analyst skill sets through training decisions, and 4) a large number of possible future demand scenarios. We provide a integer linear program … Read more

Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes

We consider optimal transport based distributionally robust optimization (DRO) problems with locally strongly convex transport cost functions and affine decision rules. Under conventional convexity assumptions on the underlying loss function, we obtain structural results about the value function, the optimal policy, and the worst-case optimal transport adversarial model. These results expose a rich structure embedded … Read more

Global Solutions of Nonconvex Standard Quadratic Programs via Mixed Integer Linear Programming Reformulations

A standard quadratic program is an optimization problem that consists of minimizing a (nonconvex) quadratic form over the unit simplex. We focus on reformulating a standard quadratic program as a mixed integer linear programming problem. We propose two alternative mixed integer linear programming formulations. Our first formulation is based on casting a standard quadratic program … Read more

Integer Models for the Asymmetric Traveling Salesman Problem with Pickup and Delivery

We propose a new Mixed Integer Programming formulation for the Asymmetric Traveling Salesman Problem with Pickup and Delivery, along with valid inequalities for the Sarin-Sherali-Bhootra formulation. We study these models in their complete forms, relax complicating constraints of these models, and compare their performance. Finally, we present computational results showing the promise of these formulations … Read more

Decision Diagram Decomposition for Quadratically Constrained Binary Optimization

In recent years the use of decision diagrams within the context of discrete optimization has proliferated. This paper continues this expansion by proposing the use of decision diagrams for modeling and solving binary optimization problems with quadratic constraints. The model proposes the use of multiple decision diagrams to decompose a quadratic matrix so that each … Read more